In this paper we introduce a notion of digital implicit surface in arbitrary dimensions. The digital implicit surface is the result of a morphology inspired digitization of an implicit surface { x ∈ R^n : f (x) = 0 } which is the boundary of a given closed subset of R^n , { x ∈ R^n : f (x) ≤ 0 } . Under some constraints, the digital implicit surface has some interesting properties, such as k-tunnel freeness. Furthermore, for a large class of the digital implicit surfaces, there exists a very simple analytical characterization.